# Matrices(inverse)

• Oct 23rd 2012, 11:00 AM
blueberry94
Matrices(inverse)
Good evening,
i have an assignment for tomorrow and i still have 2 exercises that i didn't know how to resolve them.
I will be more than grateful if someone could help me.
#1
Let A be an nxn invertible matrix. Show that if A is in upper (lower) triangular form,then A-1 is also in upper(lower) triangular form

#2
Suppose B is row equivalent to the nxn invertible matrix A.Show that B is invertible.

• Oct 23rd 2012, 11:39 AM
girdav
Re: Matrices(inverse)
Good evening.

For the first question, you can try a proof by induction on the dimension.

For the second one, how would you translate the condition of row equivalence in terms of matrices?

By the way, welcome to Math Help Forum!
• Oct 23rd 2012, 02:29 PM
hedi
Re: Matrices(inverse)
for the second part, if B is row equivalent to A,then B is obtained by multipying A by a finite number of elementary matrices,namely, B=E1E2...EkA.So B is invertible as product of invertible matrices.